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arXiv · 0706.0633

Quotients of continuous convex functions on nonreflexive Banach spaces

P. Holicky·O. Kalenda·L. Vesely·L. Zajicek
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Abstract

On each nonreflexive Banach space X there exists a positive continuous convex function f such that 1/f is not a d.c. function (i.e., a difference of two continuous convex functions). This result together with known ones implies that X is reflexive if and only if each everywhere defined quotient of two continuous convex functions is a d.c. function. Our construction gives also a stronger version of Klee's result concerning renormings of nonreflexive spaces and non-norm-attaining functionals.

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P. Holicky, O. Kalenda, L. Vesely, L. Zajicek. 2007-06-05. Quotients of continuous convex functions on nonreflexive Banach spaces. https://arxiv.org/abs/0706.0633

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